Am I a crank?
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From: Virgil on 31 Aug 2006 18:38 In article <agfef2p6s30nou8r1esb0ro754o7kmep2i(a)4ax.com>, Lester Zick <dontbother(a)nowhere.net> wrote: > On Thu, 31 Aug 2006 12:52:07 -0600, Virgil <virgil(a)comcast.net> wrote: > > > >Zick again attempts to speak authoritatively about modern mathematics > >from the depths of his almost total ignorance of it. > > > >Proclaiming 'sour grapes' about what he cannot have. > > Clever devil that you are I could scarcely do otherwise. It takes time and dedication to do otherwise, but some manage it.
From: Virgil on 31 Aug 2006 18:39 In article <4ifef25n4c3pi6fk1agfrpbljofs1im7gk(a)4ax.com>, Lester Zick <dontbother(a)nowhere.net> wrote: > On Thu, 31 Aug 2006 12:55:05 -0600, Virgil <virgil(a)comcast.net> wrote: > > >In article <v76ef2tt99t6kfnltkss0pjl1he46ndppf(a)4ax.com>, > > Lester Zick <dontbother(a)nowhere.net> wrote: > > > >> >Definitions can be false too (i.e. "Let x be an even odd"). > >> > >> Except that Virgil maintains that definitions in modern math are > >> neither true nor false. > > > >If one had said that there is an odd even, that would be declarative and > >a false declaration, but "Let x be an even odd" is not a declaration of > >presumed fact but a request, which can be denied but not falsified. > > Yes but is that true or false or just an axiom or definition? A metatheorem of logic.
From: Virgil on 31 Aug 2006 18:53 In article <0kfef21lbrjan4tjb6rq43vvt3etr8jajf(a)4ax.com>, Lester Zick <dontbother(a)nowhere.net> wrote: > On Thu, 31 Aug 2006 12:57:46 -0600, Virgil <virgil(a)comcast.net> wrote: > > >He is right, in the sense that definitions are requests to let one thing > >represent another, and while one can refuse a request, it is silly to > >call a request either true or false. > > So now it's silly to call axioms and definitions in modern math and > theorems based on them true? Calling an axiom true is not silly, but an axiom is not provably true unless the proof derives some assumptions made about what is true. Calling a definition true is silly because true or false are not possible attributes of definitions. Theorems are statements have a proof based on the axiom system in which they are theorems. Note that every theorem by definition requires an axiom system and a proof that it follows from those axioms( and "proof" means logically valid proof).
From: MoeBlee on 31 Aug 2006 18:55 Virgil wrote: > > >If one had said that there is an odd even, that would be declarative and > > >a false declaration, but "Let x be an even odd" is not a declaration of > > >presumed fact but a request, which can be denied but not falsified. > > > > Yes but is that true or false or just an axiom or definition? > > A metatheorem of logic. There is a metatheorem of logic that the expression 'let x be an even odd' is a request? MoeBlee
From: Virgil on 31 Aug 2006 19:03
In article <bofef29jedcu2em78lm1euh0cphvqur009(a)4ax.com>, Lester Zick <dontbother(a)nowhere.net> wrote: > On Thu, 31 Aug 2006 13:00:40 -0600, Virgil <virgil(a)comcast.net> wrote: > > >In article <ub6ef21d9o1m22bbhok6d0knbu12v0dt5d(a)4ax.com>, > > Lester Zick <dontbother(a)nowhere.net> wrote: > > > > > >> So how exactly do definitions differ from propositions? > > > >Definitions are requests to let one thing represent another, whereas > >propositions are declarations that something is true. > > So propositions can be true based on definitions which are not true? > Hmm, curiouser and curioser. Not quite. If a proposition containing definienda remains true when every definiendum appearing in it is replaced by its definiens, only then need it be true, but by then it is entirely independent of any definitions. |